If you run their software, yeah they can fingerprint your device. That includes if you visit their websites — it’s completely feasible to take a deterministic reading of various unique qualities of your machine that can be used to later identify your device as the same device in another circumstance. That doesn’t inherently provide lineage to anything identifying you, but it can easily lead to something.
Unless you have a very unique device, I imagine it’s not possible to do this posthoc with standard data collection from web traffic. You’d need to be intentionally doing this beforehand for it to be reliable.
Though… I wonder if there are certain softwares where telemetry can reasonable be used to fingerprint a device. Maybe a browser like Edge — though, who’s using Edge on Linux lol?